Higher Fourier Harmonics of the Directional Distribution of an Equilibrium Wave Field under Steady Wind Forcing

Abstract

Recently, directional wave spectra have been obtained by applying the two-dimensional fast Fourier transform (2D FFT) to the three-dimensional spatial topography of ocean surface waves collected by an airborne scanning laser ranging system during a quasi-equilibrium wind wave condition. The directional distributions show that most wave energy at wavenumbers larger than the peak wavenumber is in two sidelobes at directions symmetrically located about the wind direction. Presented in this study is an analysis of the Fourier harmonics derived from decomposition of the measured bimodal directional distributions. The similarity properties of the Fourier coefficients are analyzed. A nonlinear function is proposed to represent the similarity relation. A bimodal directional distribution model in the form of Fourier series expansion consisting of the first eight Fourier harmonics is developed. Application of this model to extend the directional distribution of buoy measurements is demonstrated.